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We construct a model of spontaneous CP violation in E6 supersymmetric grandunified theory. In the model, we employ an SU(2)F flavor symmetry and ananomalous U(1)A symmetry. The SU(2)F flavor symmetry is introduced to providethe origin of hierarchical structures of Yukawa coupling and to ensure theuniversality of sfermion soft masses. The anomalous U(1)A symmetry isintroduced to realize the doublet-triplet mass splitting, to provide the originof hierarchical structures of Yukawa couplings, and to solve the mu problem. Inthe model, CP is spontaneously broken by the SU(2)F breaking in order toprovide a Kobayashi-Maskawa phase and to evade the supersymmetric CP problem.However, a naive construction of the model generally leads to unwanted outcome,Arg[mu b*]=O(1), when CP violating effects in the flavor sector are taken intoaccount. We cure this difficulty by imposing a discrete symmetry and find thatthis prescription can play additional roles. It ensures that realistic up-quarkmass and Cabibbo angle are simultaneously realized without cancellation betweenO(1) coefficients. Also, severe constraints from the chromo-electric dipolemoment of the quark can be satisfied without destabilizing the weak scale. Thediscrete symmetry reduces the number of free parameters, but the model iscapable of reproducing quark and lepton mass spectra, mixing angles, and aJarlskog invariant. We obtain characteristic predictions Vub sim O(lambda^4)(lambda=0.22) and |Vcb Yb| = |Yc| at the grand unified theory scale.

Spontaneous CP violation in E6 SUSY GUT with SU(2) flavor and anomalous U(1) symmetries